What are the achievements of Logic?

What is the basis for reason? And mathematics?

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Science Fan
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Re: What are the achievements of Logic?

Post by Science Fan » Tue Feb 27, 2018 10:45 pm

Lacewing: If I had to summarize your personal philosophy, I would say it is the following: "I don't tolerate bullshit."

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Lacewing
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Re: What are the achievements of Logic?

Post by Lacewing » Tue Feb 27, 2018 11:43 pm

Science Fan wrote:
Tue Feb 27, 2018 10:45 pm
Lacewing: If I had to summarize your personal philosophy, I would say it is the following: "I don't tolerate bullshit."
:D

My Grandma used to listen thoughtfully to an explanation, and then she'd furrow her brow and say, "Cut the crap!"

I would be honored to carry on the tradition. :)

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Re: What are the achievements of Logic?

Post by Science Fan » Wed Feb 28, 2018 9:31 pm

Lacewing: Well, if you ever sneak across the border to run for president, you've got my vote.

Dalek Prime
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Re: What are the achievements of Logic?

Post by Dalek Prime » Thu Mar 01, 2018 1:47 am

Dapplegrim wrote:
Mon Nov 27, 2017 12:31 pm
What are the achievements of logic? It would seem to be hard to identify them.

In contrast mathematics has huge achievements to its name, especially its use in the domain of physics.

But logic, whether pure and abstract or its application to language, does not have many, if any, achievements to its name.

'Socrates is mortal' and 'It is raining' - two classical conclusions of logic, can hardly be claimed as achievements.

Its main claim would seem to be that it claims to be 'true'. But by what logic is that claim to truth justified? And also what is meant by 'true' when applied to logic? It would appear to be only a label to indicate internal self-consistency.

Does philosophy need this form of logic? If so what for?

Does anyone have any suggestions?
Mathematics is a subset of symbolic logic. What a silly thing to question. Try reading Suzanne Langer's 'Introduction to Symbolic Logic' before making such statements.

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Re: What are the achievements of Logic?

Post by wtf » Thu Mar 01, 2018 3:01 am

Dalek Prime wrote:
Thu Mar 01, 2018 1:47 am
Mathematics is a subset of symbolic logic.
Did you miss the memo from Gödel?

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Eodnhoj7
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Re: What are the achievements of Logic?

Post by Eodnhoj7 » Thu Mar 01, 2018 6:18 pm

Lacewing wrote:
Tue Feb 27, 2018 9:09 pm
Eodnhoj7 wrote:
Tue Feb 27, 2018 8:37 pm
Lacewing wrote:
Tue Feb 27, 2018 8:30 pm
Seriously, are you on drugs? :lol:
No, but there is no wrong in it according to you, so would it matter?
It would simply help explain your weird communication. :lol:
That is kind of hypocritical for someone open to "creative potential" and life experiences to pass judgement?
Eodnhoj7 wrote:
Tue Feb 27, 2018 8:37 pm
So there are things that are "wasteful" and things that are "not wasteful"?
Sure, in the context of what I want to invest my energy on at any given time.
So what you "want" defines what is true and not true to you?
Eodnhoj7 wrote:
Tue Feb 27, 2018 8:37 pm
Lacewing wrote:
Tue Feb 27, 2018 8:30 pm
I simply don't like the extra effort you require. :)
And that cannot change?
Sure it can. So? Why do I need to invest any more in it until it does?
You already are hooked in the conversation.
Eodnhoj7 wrote:
Tue Feb 27, 2018 7:29 pm
Here I will summarize this conversation so the point becomes clear, you claim everything changes....all people change, physical realities change, etc.
Yes, it appears to me that all things change with time and/or circumstances.
Eodnhoj7 wrote:
Tue Feb 27, 2018 7:29 pm
But when a question is posed, that either requires a form of change in thinking on your part (and you claim change is inevitable in all things), you cease to do it....hence there are certain constants.
In the moment, and depending on the circumstance, a change in thinking may not be logical.
Then you do not always change do you? And what is logical exactly, past what you want and don't want?

What is this problem you have with accepting multiple things as being true? Are you so jacked up to have a set of solid, unmovable, absolute answers -- to such a degree that you can't even function or adapt or flow? Or do you just like to argue?
Are you so jacked up to have a set of changing answer -- to such a degree that you can't even function let alone know who you are?How many "identities" have you been through at this point? Do you even know who you are, or do you just respond to whatever changes come along?
Eodnhoj7 wrote:
Tue Feb 27, 2018 7:29 pm
You also claim to "embrace" everything there is in the human experience, but seem "uncomfortable" (at least that is how it appears to me), walking down certain experiences.
Yes, both true. I do try to embrace everything in the human experience, but some things (like your stupid questions) are uncomfortable to continually wade through over and over, droning on and on, seemingly without end. Still, look at the effort I've made! :D
In all truth, I am not really impressed by your efforts, you seem like you are trying to please me, or someone...whatever.... To be quite frank the whole "multiple" experience argument usually equates to "I have had multiple jobs and multiple lovers all of which came and go, I have no control, I don't even know who I am anymore because of all the experiences, so I just let life use me for what it wants".


Several threads ago, I argue a standard time and place for everything argument. You agreed, however that argument strictly observes a constant, that what we understand of certain phenomena have a time and place (which is absolute) and when taken out of that proper time and place they cease to exist.

Eodnhoj7 wrote:
Tue Feb 27, 2018 7:29 pm
To sum up these arguments, it appears the philosophy you are espousing does not appear to work for you, hence why argue it to others?
Yeh, whatever. You clearly don't understand half of what I say... so I'm not real surprised by your conclusion.

I don't think I am the only one who does not understand what you have to say...you are just a secular version of Nick. The whole "beauty in everything" approach seems like a cop out to not step outside you comfort zone.
Eodnhoj7 wrote:
Tue Feb 27, 2018 7:29 pm
This is just an exercise in the practical aspect of thinking and self-reflection, take it for what it is.
I did. Are we done here?
If we were done, you wouldn't have bother responding.

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Re: What are the achievements of Logic?

Post by Eodnhoj7 » Thu Mar 01, 2018 6:20 pm

Lacewing wrote:
Tue Feb 27, 2018 9:21 pm
Eodnhoj7 wrote:
Tue Feb 27, 2018 8:51 pm
Lacewing wrote:
Tue Feb 27, 2018 8:46 pm
There are definitely some crazy things that are said on this forum. Sometimes it's unfathomable how people could come up with such things. The way I've evolved to accept and understand it is to be amazed and amused at the creative potential. Sometimes it's easier than other times... but the more you do it, the easier it gets... and I've gotten pretty good at it. :D
Good then maybe you could explain your philosophy to me then...considering you claim I don't understand it.
As usual, you don't follow... What I've gotten good at is accepting and understanding the insane ramblings of people like you, by evolving to be amazed and amused at the creative potential.

Now, I'm done explaining obvious things to you. My energy is better used elsewhere.
The only point I am arguing, relative to logic is this:

There are constants, and what we understand of the constants is merely change as a form of approximation of the constants. Change exists as approximation however it is not a complete nor total truth in itself.

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Re: What are the achievements of Logic?

Post by Dalek Prime » Sat Mar 03, 2018 5:57 am

wtf wrote:
Thu Mar 01, 2018 3:01 am
Dalek Prime wrote:
Thu Mar 01, 2018 1:47 am
Mathematics is a subset of symbolic logic.
Did you miss the memo from Gödel?
No. I just used it to wipe my butt. Tell Kurt to send it again.

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Re: What are the achievements of Logic?

Post by wtf » Sat Mar 03, 2018 7:46 pm

Dalek Prime wrote:
Sat Mar 03, 2018 5:57 am
No. I just used it to wipe my butt. Tell Kurt to send it again.
So you're ignorant and proud of it? I don't follow your logic or rhetorical style. The incompleteness theorem destroyed the logicist program in 1931.

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Re: What are the achievements of Logic?

Post by wtf » Sat Mar 03, 2018 11:49 pm

Dalek Prime wrote:
Sat Mar 03, 2018 5:57 am

No. I just used it to wipe my butt. Tell Kurt to send it again.
ps -- Perhaps underneath that moronic response was a genuine curiosity about logicism.

From Wikipedia:

Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.

...

Kurt Gödel's incompleteness theorem undermines logicism because it shows that no particular axiomatization of mathematics can decide all statements. Some believe that the basic spirit of logicism remains valid because that theorem is proved with logic just like other theorems. However, that conclusion fails to acknowledge any distinction between theorems of first-order logic and those of higher-order logic. The former can be proven using the fundamental theorem of arithmetic (see Gödel numbering), while the latter must rely on human-provided models. Tarski's undefinability theorem shows that Gödel numbering can be used to prove syntactical constructs, but not semantic assertions. Therefore, any claim that logicism remains a valid concept relies on the dubious notion that a system of proof based on man-made models is as authoritative as one based on the existence and properties of the natural numbers.


If you have any more questions as to why we now know that math is NOT reducible to logic, feel free to post about wiping your butt. It makes us all very impressed with your intelligence.

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Re: What are the achievements of Logic?

Post by A_Seagull » Sun Mar 04, 2018 12:12 am

wtf wrote:
Sat Mar 03, 2018 11:49 pm
Dalek Prime wrote:
Sat Mar 03, 2018 5:57 am

No. I just used it to wipe my butt. Tell Kurt to send it again.
ps -- Perhaps underneath that moronic response was a genuine curiosity about logicism.

From Wikipedia:

Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.

...

Kurt Gödel's incompleteness theorem undermines logicism because it shows that no particular axiomatization of mathematics can decide all statements. Some believe that the basic spirit of logicism remains valid because that theorem is proved with logic just like other theorems. However, that conclusion fails to acknowledge any distinction between theorems of first-order logic and those of higher-order logic. The former can be proven using the fundamental theorem of arithmetic (see Gödel numbering), while the latter must rely on human-provided models. Tarski's undefinability theorem shows that Gödel numbering can be used to prove syntactical constructs, but not semantic assertions. Therefore, any claim that logicism remains a valid concept relies on the dubious notion that a system of proof based on man-made models is as authoritative as one based on the existence and properties of the natural numbers.


If you have any more questions as to why we now know that math is NOT reducible to logic, feel free to post about wiping your butt. It makes us all very impressed with your intelligence.

From a philosophical perspective, why is it necessary - or even desirable - for all statements of mathematics to be decidable?

What determines whether any particular statement (string of symbols) is mathematical or not?

If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely non-problematic.

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Re: What are the achievements of Logic?

Post by wtf » Sun Mar 04, 2018 12:15 am

A_Seagull wrote:
Sun Mar 04, 2018 12:12 am
If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely non-problematic.
When did I say undecidability is "problematic?"

I simply pointed out the extremely well known fact that Gödel's 1931 incompleteness theorems destroyed the hopes of the logicists.

From that moment on, the claim that "math is reducible to logic" is simply false.

I gave the Wikipedia reference but anyone can consult SEP or any textbook on mathematical logic. This isn't a controversial issue, it's a standard fact.

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Re: What are the achievements of Logic?

Post by A_Seagull » Sun Mar 04, 2018 2:19 am

wtf wrote:
Sun Mar 04, 2018 12:15 am
A_Seagull wrote:
Sun Mar 04, 2018 12:12 am
If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely non-problematic.
When did I say undecidability is "problematic?"

I simply pointed out the extremely well known fact that Gödel's 1931 incompleteness theorems destroyed the hopes of the logicists.

From that moment on, the claim that "math is reducible to logic" is simply false.

I gave the Wikipedia reference but anyone can consult SEP or any textbook on mathematical logic. This isn't a controversial issue, it's a standard fact.
I wasn't trying to argue with you!

I was just making inferences from Godel's conclusion.

Would you like to comment on my conclusion?

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Re: What are the achievements of Logic?

Post by wtf » Sun Mar 04, 2018 4:05 am

A_Seagull wrote:
Sun Mar 04, 2018 2:19 am
I wasn't trying to argue with you!
Oh ok my misunderstanding.
A_Seagull wrote:
Sun Mar 04, 2018 2:19 am
I was just making inferences from Godel's conclusion.
Incompleteness/undecidability are fantastically problematic They lead to many philosophical questions. Like, what is truth? If reason can't lead to truth then the Western project is doomed. That's why the postmodernists are winning these days. The societal rejection of reason comes straight from math itself.

* From non-Euclidean geometry we know that math can't tell us what's true. It depends on your axioms.

* And ‎Gödel told us that even when we choose a set of axioms, we still can't know what's true!

What is true? Rationality cannot tell us. Western civilization is at risk. Pick up a newspaper. Intersectionality is in; rationality is out.

Tell me, what do you think of my thesis? That non-Euclidean geometry and Gödel's incompleteness theorem are the root cause of the contemporary labelling of rationality itself as a tool of social oppression rather than one of human liberation?
A_Seagull wrote:
Sun Mar 04, 2018 2:19 am
Would you like to comment on my conclusion?
Ok! You wrote:
A_Seagull wrote:
Sun Mar 04, 2018 2:19 am
If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely non-problematic.
It's terribly problematic. We can no longer rely on reason to know what's true. There's a straight line from Riemann and Gödel to the suppression of free speech by social justice warriors.

The entire Western tradition is at stake. Euclid's project has failed.

And look here. I have a datapoint for you. It's from an alt-right website but there's no reason to believe the information is false. If you hate alt-right websites I'll stipulate to your objection and you can forget I mentioned it. But it's out there, it's apparently true, and it's pretty depressing if one is a rationalist.

Students enrolled in a Physics 101 course at Pomona College last semester were required to complete a "Decolonizing Physics" project by calling attention to issues like "implicit bias" and "microaggressions."

https://www.campusreform.org/?ID=10586

I say this is the result of the lost of faith in rationality due to non-Euclidean geometry and incompleteness.

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Re: What are the achievements of Logic?

Post by A_Seagull » Mon Mar 05, 2018 5:56 am

wtf wrote:
Sun Mar 04, 2018 4:05 am
A_Seagull wrote:
Sun Mar 04, 2018 2:19 am
I wasn't trying to argue with you!
Oh ok my misunderstanding.
A_Seagull wrote:
Sun Mar 04, 2018 2:19 am
I was just making inferences from Godel's conclusion.
Incompleteness/undecidability are fantastically problematic They lead to many philosophical questions. Like, what is truth? If reason can't lead to truth then the Western project is doomed. That's why the postmodernists are winning these days. The societal rejection of reason comes straight from math itself.

* From non-Euclidean geometry we know that math can't tell us what's true. It depends on your axioms.

* And ‎Gödel told us that even when we choose a set of axioms, we still can't know what's true!

What is true? Rationality cannot tell us. Western civilization is at risk. Pick up a newspaper. Intersectionality is in; rationality is out.

Tell me, what do you think of my thesis? That non-Euclidean geometry and Gödel's incompleteness theorem are the root cause of the contemporary labelling of rationality itself as a tool of social oppression rather than one of human liberation?
A_Seagull wrote:
Sun Mar 04, 2018 2:19 am
Would you like to comment on my conclusion?
Ok! You wrote:
A_Seagull wrote:
Sun Mar 04, 2018 2:19 am
If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely non-problematic.
It's terribly problematic. We can no longer rely on reason to know what's true. There's a straight line from Riemann and Gödel to the suppression of free speech by social justice warriors.

The entire Western tradition is at stake. Euclid's project has failed.

And look here. I have a datapoint for you. It's from an alt-right website but there's no reason to believe the information is false. If you hate alt-right websites I'll stipulate to your objection and you can forget I mentioned it. But it's out there, it's apparently true, and it's pretty depressing if one is a rationalist.

Students enrolled in a Physics 101 course at Pomona College last semester were required to complete a "Decolonizing Physics" project by calling attention to issues like "implicit bias" and "microaggressions."

https://www.campusreform.org/?ID=10586

I say this is the result of the lost of faith in rationality due to non-Euclidean geometry and incompleteness.
It would seem to come down to what one wants from philosophy and perhaps what one expects from philosophy. And if there are expectations, what are those expectations and are they justified and if so how are they justified.

For me, truth is a label and there needs to be a process by which ideas or statements are labelled as 'true'.

So for mathematics the theorems of the system, which are deduced from the axioms, can be labelled as 'true' albeit only within the system of mathematics.

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